The following is the updated "set list" of shipboard work-songs claimed to have existed up through the 1880s. Re: number of appearances, I have made an effort to excluded from the tally any citations that were clearly repetitions of prior text sources. There are 101 chanties here. The usual disclaimers about vague references, subjectivity in tally, etc. apply. Remember, these are only ship-board songs.

ACROSS THE WESTERN OCEAN (4)
A-ROVING (2)
And England's blue for ever"
Baltimore Bell"
Black although she be"
BLACKBALL LINE (4)
BLOW BOYS BLOW (5)
BLOW THE MAN DOWN (9)
BONEY (4)
BOTTLE O (1)
BOWLINE (9)
BULLY IN ALLEY (1)
BUNCH OF ROSES (1)
Captain gone ashore!"
Cheerily she goes"
CHEERLY (13)
CLEAR THE TRACK (1)
DEAD HORSE (3)
DRUNKEN SAILOR (2)
FIRE FIRE (2)
GOLDEN VANITY (1)
GOOD MORNING LADIES (2)
GOODBYE FARE YOU WELL (7)
GOODBYE MY LOVE (2)
GROG TIME (1)
Hah, hah, rolling John" (1)
Hand ober hand, O"
HANDY MY BOYS (2)
HANGING JOHNNY (3)
HAUL AWAY JOE (8)
Heave and she goes, stamp and she goes"
HEAVE AWAY MY JOHNNIES (6)
Heave her away"
Heave him up! O he yo!"
Heave round hearty!"
Heave, to the girls!"
HIGHLAND (2)
Highland day and off she goes"
HILO BOYS (3)
HILONDAY (1)
HOGEYE (1)
Ho, O, heave O"
HOOKER JOHN (1)
HUCKLEBERRY HUNTING (1)
HUNDRED YEARS (3)
Hurrah! hurrah! my hearty bullies!"
Jack Cross-tree,"
JOHN BROWN'S BODY (1)
John, John Crow is a dandy, O"
JOHNNY BOWKER (3)
Johnny's gone"
Land ho"
Largy Kargy"
LEAVE HER JOHNNY (2)
LOWLANDS AWAY (3)
Miranda Lee"
MOBILE BAY (1)
MONEY DOWN (2)
MR. STORMALONG (6)
Nancy Bell"
Nancy oh!"
NEW YORK GIRLS (2)
O ee roll & go"
O! hurrah my hearties O!"
Oceanida"
Oh fare you well, my own Mary Anne"
OH RILEY (1)
Oh Sally Brown, Sally Brown, oh!"
ONE MORE DAY (1)
OUTWARD AND HOMEWARD BOUND (3)
PADDY DOYLE (3)
PADDY LAY BACK (1)
PADDY ON THE RAILWAY (5)
Pull away now, my Nancy, O!"
REUBEN RANZO (9)
RIO GRANDE (6)
ROUND THE CORNER (3)
RUN LET THE BULGINE RUN (3)
SACRAMENTO (3)
SAILOR FIREMAN (1)
SALLY BROWN (6)
Sally in the Alley"
SANTIANA (9)
SHALLOW BROWN (1)
SHENANDOAH (8)
SLAPANDER (1)
Sing, Sally, ho!"
SOUTH AUSTRALIA (1)
STORMALONG JOHN (1)
STORMY (9)
STORMY ALONG (2)
TALLY (2)
Time for us to go!"
TOMMY'S GONE (3)
Up a hill"
Walk away"
WALKALONG SALLY (1)
When first we went a-waggoning"
WHISKEY JOHNNY (10)
Whisky for Johnny!"
YEO HEAVE HO (1)

The most frequently appearing items overall are:

CHEERLY (13)
WHISKEY JOHNNY (10)
STORMY / BOWLINE / BLOW THE MAN DOWN / REUBEN RANZO / SANTIANA (9) SHENANDOAH / HAUL AWAY JOE (8)